The diagram shows two parallel lines intersected by a transversal, creating several angles. The angle labeled $48^\circ$ is given, and the angle labeled $x^\circ$ is the unknown angle we need to find.

Since the two lines are parallel and the third line acts as a transversal, the angles $x^\circ$ and $48^\circ$ are alternate interior angles, which are always congruent.

Therefore, we can conclude: $x^\circ = 48^\circ$

Thus, the value of $x$ is $48^\circ$.

Would you like further details or have any questions?

Here are some related questions to consider:

1. What are alternate interior angles?
2. How can you identify corresponding angles in parallel lines?
3. How are vertically opposite angles related?
4. What are supplementary angles and how do they appear in parallel line setups?
5. Can we use these principles with non-parallel lines?

Tip: When two parallel lines are cut by a transversal, alternate interior angles are always equal.